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When you throw an object, you do apply a force. However, don't forget that you only apply this force as long as you're in contact with the object. Once it has left your hand, there is no more force acting on the object (at least in a vacuum). Therefore there will be no acceleration on the object and it will just keep going with the same velocity it had when it left your hand.

Concerning your question about where your force went. In a very literal sence, the force you applied is still present in the object as kinetic energy. This energy can be calculated as $$E = \frac{1}{2}mv^2$$ as long as $v \ll c$. It is this energy that determines how much force you need to slow the object back down to rest in the same distance as it was accelerated by you.